This is a scale drawing of an actual park. What percent of the park is the playground?

Start by finding the area of the entire park on the map.
A scale map of a park with dimensions 20 in by 20 in. Within the park are a picnic area and a playground with dimensions 16 in by 5 in.
The area of the entire park is
square in.

1 answer

To find the area of the entire park on the map, we can use the formula for the area of a rectangle:

\[ \text{Area} = \text{length} \times \text{width} \]

For the park, the dimensions are 20 inches by 20 inches:

\[ \text{Area of the park} = 20 , \text{in} \times 20 , \text{in} = 400 , \text{square inches} \]

Next, we can calculate the area of the playground, which has dimensions 16 inches by 5 inches:

\[ \text{Area of the playground} = 16 , \text{in} \times 5 , \text{in} = 80 , \text{square inches} \]

To find the percentage of the park that is the playground, we use the following formula:

\[ \text{Percentage of park that is playground} = \left( \frac{\text{Area of playground}}{\text{Area of park}} \right) \times 100 \]

Substituting the areas we calculated:

\[ \text{Percentage of park that is playground} = \left( \frac{80 , \text{square inches}}{400 , \text{square inches}} \right) \times 100 = 20% \]

Therefore, the area of the entire park is 400 square inches, and the playground occupies 20% of the park.